🚀 go-pugleaf

Here is an interesting postscript program which generates the
Sierpinski gasket using the chaos game.

------------------------ CUT HERE --------------------------------
%!
% chaos.ps: The chaos game
% Reference: Fractals For the Classroom, by Peitgen, Jurgens and Saupe
% Author: Barry G. Adams (barry@ramsey.cs.laurentian.ca)

% Procedure for plotting a pixel
1 setlinecap
0.2 setlinewidth
/plotpixel { moveto 0.2 0 rlineto stroke} def

% getting random integer array index 0, 1, or 2
/randindex {rand 3 mod} def

% triangle vertices
/xvertices [100 520 310] def
/yvertices [100 100 380] def

% procedure for computing average of two numbers
/avg { add 2 div } def

% Procedure for drawing triangle outline
/triangle {
   newpath
      xvertices 0 get yvertices 0 get moveto
      xvertices 1 get yvertices 1 get lineto
      xvertices 2 get yvertices 2 get lineto 
   closepath
   stroke
} def

% Play the game:
% (1) Initialize a current point
% (2) randomly generate a triangle vertex number (0, 1, 2),
% (3) calculate the midpoint of the line joining this vertex
%     to the current point, plot the midpoint and make it the
%     new current point.
% (4) go to (2)
/playgame {
   /numpoints exch def % get number of points
   % initialize the current point
   /cpx xvertices 0 get xvertices 1 get avg def
   /cpy yvertices 0 get yvertices 2 get avg def
   triangle
   cpx cpy plotpixel
   numpoints {
      /r randindex def
      /cpx xvertices r get cpx avg def
      /cpy yvertices r get cpy avg def 
      cpx cpy plotpixel
   } repeat
} def

/Times-Roman findfont 24 scalefont setfont
100 710 moveto (The Chaos Game: Sierpinski Surprise) show
/Times-Roman findfont 12 scalefont setfont
/str 30 string def

% Play the game with 1000 points
/numpoints 1000 def
gsave
   0 300 translate
   numpoints playgame
   100 300 moveto numpoints str cvs show ( points) show
grestore

% Play the game with 40000 points
/numpoints 40000 def
gsave
   0 0 translate
   numpoints playgame
   100 300 moveto numpoints str cvs show ( points) show
grestore
showpage